Time-correlation functions for odd Langevin systems
Abstract
We investigate the statistical properties of fluctuations in active systems that are governed by non-symmetric responses. Both an underdamped Langevin system with an odd resistance tensor and an overdamped Langevin system with an odd elastic tensor are studied. For a system in thermal equilibrium, the time-correlation functions should satisfy time-reversal symmetry and the anti-symmetric parts of the correlation functions should vanish. For the odd Langevin systems, however, we find that the anti-symmetric parts of the time-correlation functions can exist and that they are proportional to either the odd resistance coefficient or the odd elastic constant. This means that the time-reversal invariance of the correlation functions is broken due to the presence of odd responses in active systems. Using the short-time asymptotic expressions of the time-correlation functions, one can estimate an odd elastic constant of an active material such as an enzyme or a motor protein.
Cite
@article{arxiv.2202.03225,
title = {Time-correlation functions for odd Langevin systems},
author = {Kento Yasuda and Kenta Ishimoto and Akira Kobayashi and Li-Shing Lin and Isamu Sou and Yuto Hosaka and Shigeyuki Komura},
journal= {arXiv preprint arXiv:2202.03225},
year = {2022}
}